Question

(3-✓2)^2-6*(3-✓2)+7 решить поэтапно

Answer 1

(3-√2)^2-6(3-√2)+7= 9-6√2+2-18+6√2+7=0

Answer 2

To solve the expression (3-√2)^2 - 6*(3-√2) + 7 step-by-step, follow these steps:

Step 1: Simplify the squared term (3-√2)^2 = (3-√2) * (3-√2) Using the formula (a-b)^2 = a^2 - 2ab + b^2, where a = 3 and b = √2: (3-√2)^2 = 3^2 - 2 * 3 * √2 + (√2)^2 (3-√2)^2 = 9 - 6√2 + 2 (because √2 * √2 = 2) (3-√2)^2 = 11 - 6√2

Step 2: Simplify the expression further Now we have (3-√2)^2 - 6*(3-√2) + 7 Substitute the value we found in Step 1: (11 - 6√2) - 6*(3-√2) + 7

Step 3: Distribute the -6 to both terms inside the parentheses: (11 - 6√2) - (63 - 6√2) + 7

Step 4: Simplify the expression inside the parentheses: (11 - 6√2) - (18 - 6√2) + 7

Step 5: Now combine like terms: 11 - 6√2 - 18 + 6√2 + 7

Step 6: Combine constants and like terms with √2: (-6√2 + 6√2) + (11 - 18 + 7)

Step 7: The √2 terms cancel out, and we are left with: 0 + 0

Step 8: Finally, simplify the expression: 0

So, the solution to the expression (3-√2)^2 - 6*(3-√2) + 7 is 0.